a1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. e-mail: [email protected]
a2 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. e-mail: [email protected]
For a finite group G, let F2(G) be the number of factorizations G = AB of the group G, where A and B are subgroups of G. We compute F2(G) for certain classes of groups, including cyclic groups ℤn, elementary abelian p-groups ℤpn, dihedral groups D2n, generalised quaternion groups Q4n, quasi-dihedral 2-groups QD2n(n≥4), modular p-groups Mpn, projective general linear groups PGL(2, pn) and projective special linear groups PSL(2, pn).
(Received August 16 2011)
(Accepted September 24 2011)
(Online publication December 12 2011)
2000 Mathematics Subject Classification